Review of representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification. Rational numbers as recurring/terminating decimals.

Examples of nonrecurring / non terminating decimals such as v2, v3, v5 etc. Existence of non-rational numbers (irrational numbers) such as v2, v3 and their representation on the number line.

Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.

Existence of vx for a given positive real number x (visual proof to be emphasized).

Definition of nth root of a real number.

Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

Rationalization (with precise meaning) of real numbers of the type (& their combinations)where x and y are natural number and a, b are integers.

UNIT II : ALGEBRA

1. POLYNOMIALS

(25) Periods

Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial / equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization

of ax2 + bx + c, a1 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.

Recall of linear equations in one variable. Introduction to the equation in two variables. Prove that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

UNIT III : COORDINATE GEOMETRY

1.COORDINATE GEOMETRY

(9) Periods

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y = mx + c and linking with the chapter on linear equations in two variables.

UNIT IV : GEOMETRY

1. INTRODUCTION TO EUCLID'S GEOMETRY

(6) Periods

History - Euclid and geometry in India. Euclid's method of formalizing observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem.

1. Given two distinct points, there exists one and only one line through them.

2. (Prove) two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES

(10) Periods

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180o and the converse.

2. (Prove) If two lines intersect, the vertically opposite angles are equal.

History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability.(A large amount of time to be developed to group and to individual activities to motivate the concept; the experiment to be drawn from real - life situations, and from example used in the chapter on statistics).

Have you noticed small children struggling to carry their school bags filled with books? Do you know what happens to our children when they lift the Weight that is half their weight every day?
In the...

The CBSE board is expected to release the class 10th and 12th compartment exam results on 10 August 2017. Once the results are officially declared it will be available via website http://cbseresults....